Abstract
In this paper, we have studied cyclic codes over the ring [Formula: see text], [Formula: see text]. We have provided the general form of the generators of a cyclic code over [Formula: see text] and obtained a minimal spanning set for such codes and determined their ranks. We have determined a necessary condition and a sufficient condition for cyclic codes over [Formula: see text] to be [Formula: see text]-free. For [Formula: see text], we have shown that [Formula: see text] is a local ring, and the complete ideal structure of [Formula: see text] is determined. Some examples are presented.
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